There is a great trailer forum on this site that I frequent...those folks could answer your 'increasing capacity' question very accurately. If they don't own a Kubota, they may not pick up on this thread.
I've lived the dream with a 5' x 10' single axle trailer and did not enjoy it one bit for a vast variety of reasons.
There is a very slight chance that going 6' wide would make the trailer a bit more stable, but I'm not sure. I know my 5' wide trailer (rated at 3,500# capacity) was extremely tippy.
Another thing I'd consider VERY strongly is the lack of brakes. Pulling my 5' x 10' trailer sans brakes with my
BX2230 with FEL and BoxBlade strapped thereon, my Expedition (capable of towing 9,000# with 4 piston floating calipers on huge vented disks in front and pretty good size pie dishes in back) had a small amount of trouble stopping the whole rig. Surprisingly heavy.
Though it seems like overkill for your truck, I'd get the lightest dual axle trailer you can find with wood deck and brakes on at least one axle. It will probably be rated for 7,000#, but just don't load it beyond the capabilities of your truck.
If you have one blowout or otherwise mess up using a small trailer (anything under 14' long and anything with a single axle I'm classifying as 'small'), adding the other $500 to get to a dual axle trailer will seem like the best money known to man.
Just my thoughts from past experience.